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Let the vectors PQ,OR,RS,ST,TU and UP re...

Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular hexagon.
Statement I: `PQxx(RS+ST)ne0`
Statement II: `PQxxRS=0 and PQxxSTne0`

A

Both Statement-I and Statement-II are correct and Statement-II is the correct explanation of Statement-I

B

Both Statement-I and Statement-II are correct but Statement-II is not the correct explanation of Statement-I

C

Statement-I is correct but Statement-II is incorrect

D

Statement-II is correct but Statement-I is incorrect

Text Solution

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The correct Answer is:
C
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Given : A circle, 2x^2+""2y^2=""5 and a parabola, y^2=""4sqrt(5)""x . Statement - I : An equation of a common tangent to these curves is y="x+"sqrt(5) Statement - II : If the line, y=m x+(sqrt(5))/m(m!=0) is their common tangent, then m satisfies m^4-3m^2+""2""=0. (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

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Assertion: Minimum number of non-equal Vectors in a plane required to give zero resultant is three. Reason: If vec(A)+vec(B)+vec(C )= vec(0) , then they must lie in one plane A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for statement-I B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for statement-I C. Statement-I is true, Statement-II is false. D. Statement-I is false and Statement-II is true.

Statement I. The four straight lines given by 6x^2+5xy-6y^2=0 and 6x^2+5xy-6y^2-x+5y-1=0 are the sides of a square . Statement II . The lines represented by general equation of second degree ax^2+2hxy+by^2+2gx+2fy+c=0 are perpendicular if a+b=0 .

Let A_1 A_2 A_3 A_4 A_5 A_6 A_1 be a regular hexagon. Write the x-components of the vectors representeed by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that cos0+cospi/3+cos(2pi)/3+cos(4pi)/3+cos(5pi)/3=0 Use the known cosine values of verify the result. .

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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The edges of a parallelopiped are of unit length and are parallel to ...

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  2. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

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  3. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

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  4. The number of distinct real values of lambda , for which the vectors...

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  5. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

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  6. Let vec A be a vector parallel to the line of intersection of plan...

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  7. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

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  8. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

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  9. The value of a so that the volume of parallelepiped formed by hat i...

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  10. If vec a=( hat i+ hat j+ hat k), vec a. vec b=1a n d vec axx vec b= h...

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  11. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  12. If veca and vecb are two unit vectors such that veca + 2vecb and 5 vec...

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  13. Let a= 2hat(i) -2hat(k) , b=hat(i) +hat(j) and c be a vectors suc...

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  14. If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is equal to

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  15. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

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  16. Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p...

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  17. veca =1/sqrt(10)(3hati + hatk) and vecb =1/7(2hati +3hatj-6hatk), then...

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  18. The vectors vec a and vec b are not perpendicular and vec c and v...

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  19. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

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  20. Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...

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